*Seagliders are buoyancy driven Autonomous Underwater Vehicles used for long-term oceanographic observation. How does the depth of operation affect a Seaglider’s range?*

Since Henry Strommel first posited the idea in the 1989 article “The Slocum Mission” [1], the use of buoyancy as the primary means of propulsion has become common practice for a whole class of vehicles, commonly referred to as seagliders. Autonomous underwater gliders are a family of underwater vehicles, used for long-range, long-term observation of oceanic environments. They leverage changes in net-buoyancy to generate forward locomotion through hydrodynamic surfaces. In order to function for extended periods, these systems operate in a low-speed, low-drag regime. Inherent in this method of propulsion is the need to change depth, with longer deeper dives yielding greater forward progress. However, as is the nature of buoyancy engine vehicles, the deeper the dive the more energy that is required to surface again. At what point is the added range no longer worth the requisite complexity for operation at that depth, and how do the non-propulsive systems influence this?

**How a glider works**

To propel itself, a glider uses the combination of buoyancy modulation and lifting surfaces in a series of triangular vertical maneuvers called yos (Figure 1). At the top of a typical yo cycle, the vehicle needs to reduce its buoyancy in order to sink. It accomplishes this by reducing its displaced volume; the simplest approach to this is pumping fluid onboard into its buoyancy engine. To minimize the energy required by the engine, the change in vehicle volume is small, typically no more than a few percent of total displaced volume. When the vehicle reaches the bottom of the dive, it pumps fluid out of the buoyancy engine, increasing the vehicle’s displacement. This phase of operation requires a substantial input of energy since the buoyancy engine must overcome the significant hydrostatic pressure at depth.

In spite of this large energy expenditure, seagliders operate with a high efficiency because the buoyancy engine only operates twice per cycle, once at the top and bottom of each yo, resulting in a low average propulsive power. However, the small volume changes result in small net buoyant forces, which is the vehicle’s propulsive force. These small propulsive forces result in the vehicles operating at low speeds, typically on the order of 0.3 meters per second. Operating at low speeds reduces the drag penalties incurred allowing the vehicles to have long mission durations.

**Glider power consumption**

A glider’s forward motion is a result of its change in buoyancy, which in conjunction with the glider’s wing results in its motion through the fluid. Once the vehicle achieves steady-state, the net propulsive force is equal to the energy lost to the hydrodynamic drag. It should be noted that due to the slow speeds the vehicle quickly achieves steady-state conditions. As the vehicle spends only a small percentage of the time in non-steady-state conditions (mainly at the top and bottom of each yo), we will analyze the vehicle operating under steady-state conditions. For the remainder of this analysis, data from Table 1 Glide 1 from, Graver and Leonard [2] is used. The selected data was collected during the parameterizing a Slocum glider operating in the ocean.

The buoyant force is conservative and therefore the work done by the force, moving the glider, is independent of the path taken, [3]. This work is equal to the external hydrostatic pressure multiplied by the net change in the buoyancy engines volume. To complete one full glide yo, the buoyancy engine must operate twice, once at the surface and once at depth.

Theoretically, the energy required at the surface should be zero or negative as the seawater stored in the buoyancy engine from its previous dive is at a higher pressure than the fluid surrounding it, and sinking is a low energy operation for a vehicle to undertake. However, the delicate bellows pump used by the Slocum glider, requires both a brake and regulated exhaust of stored fluid to prevent damage to the buoyancy engine. Based on the work of Bachmayer and Williams, the energy expended at the surface is assumed to be a constant value of 164 Joules [4]. Using data from [5], a buoyancy engine efficiency of 50 percent at depth and information from Claus et al [6], the overall propulsive energy per cycle is readily determined.

In order to determine the hotel load (power used to operate onboard systems, and sensors which are non-propulsive in nature) of the glider during operation, data from [6] is used in conjunction with the overall glide time of the platform per cycle. Once the energy use of the buoyancy engine is evaluated, the hotel load is added. The result of this is the total energy used per yo, and dividing this value into the energy storage of the glider results in a total number of yos achievable. Using an operational depth of 200 meters and a glide angle of 20 degrees, the distance covered per yo of 1169.73 meters and a maximum propulsion only range is determined. Multiplying the number of cycles by the horizontal distance covered results in an estimate of the vehicles overall range. Results of this are in, Table 2, with data calculated at varying depths.

Using this method, the estimated total horizontal range of 1589.53 kilometers was estimated, which matches will with the estimated Slocum range of approximately 1,500 kilometers, under the same conditions from the work done by Bachmayer and Williams [6].

**Seaglider range versus operational depth**

Seagliders operate efficiently by using their propulsive systems for a short period when compared to the time they are in motion resulting from this expenditure. Typically, to complete one cycle, or yo, a seaglider’s buoyancy engine operates for approximately 1 minute. When operating at a lower depth of 200 meters with a glide path angle of 20 degrees, this 1 minute of work results in almost an hour of forward motion. The key operational limitations on a systems range are buoyancy engine duty cycle, buoyancy engine energy expenditure at depth, and hotel load.

Due to the constant load at the surface, seagliders consume more energy when operating in repeated shallow dives. This constant load has a negative impact on overall range, regardless of sensor load. Figure 2 shows the impact of depth and sensor load on the overall range of a seaglider, with sensor loading being adjusted from full-time operation, half-time operation, to no sensor function. This clearly highlights the correlation between shallow water buoyancy engine duty cycle cost and the energy required to operate the engine at depth, and how these two tradeoff with depth. At depths approaching 50 meters, the propulsive load dominates the energy usage. After this, the hotel load dominates the energy usage. This trend along with the range and depth are highlighted in Figure 3. For the first 100 meters, the duty cycle of the engine and its associated costs dominate range. However, as depth increases, the energy required to operate the engine at depth begins to dominate largely negating any range benefits the longer glides and lower duty cycle would have.

An interesting question arises when considering the working efficiencies of conventionally propelled systems at the operating speeds typical of gliders. Can a conventionally propelled system of similar size and design compete in terms of endurance and operational range as a glider? If so, how, and will this open up bodies of water previously inaccessible to the long-term operations typical of buoyancy driven gliders?

**References**

[1] | H. Strommel, “The Slocum Mission,” Oceanography, pp. 22-25, 1989. |

[2] | J. G. Graver and N. E. Leonard, “Underwater Glider Dynamics and Control,” 12th International Symposium on Unmanned Untethered Submersible Technology, pp. 1710-1742, 2001. |

[3] | D. Keeports, “The common forces: conservative or nonconservative?,” Physics Education, vol. 41, no. 3, pp. 219-222, 2006. |

[4] | M. Krieg and K. Mohseni, “On the Propulsive Efficiency of Unsteady Propulsors,” in Third International Symposium on Marine Propulsors, Launceston, 2013. |

[5] | R. E. Davis, C. C. Ericksen and C. P. Jones, “Autonomous Buoyancy-driven Underwater Gliders,” in Technology and Applications of Autonomous Underwater Vehicles, London, Taylor & Francis Group, 2002, p. 47. |

[6] | B. Claus, R. Bachmayer and C. D. Williams, “Development of an auxiliary propulsion module for an autonomous underwater glider,” in Proceedings of the Institution of Mechancial Engineers, 2010. |

[7] | I. H. Abbott and A. E. Von Doenhoff, Theory of Wing Sections Including a Summary of Airfoil Data, New York: Dover Publications, 1949. |

[8] | J. G. Graver, R. Bachmayer, N. E. Leonard and D. M. Fratantoni, “Underwater Glider Model Parameter Identification,” in Proc. 13th Int. Symposium on Unmanned Untethered Submersible Technology, Durham, NH, 2003. |

[9] | C. D. Williams, R. Bachmayer and B. de Young, “Progress in Predicting the Performance of Ocean Glider from At-Sea Measurements”. |

Christopher Hockley is a mechanical engineering Ph.D. student at Embry-Riddle Aeronautical University working on autonomous and unmanned vehicle systems.

Dr. Brian Butka is an associate professor of electrical and computer engineering at Embry-Riddle Aeronautical University. His areas of research include communications, safety-critical hardware, and autonomous and unmanned vehicle systems.